T-Duality Simplifies Bulk–Boundary Correspondence: Some Higher Dimensional Cases

Recently we introduced T-duality in the study of topological insulators, and used it to show that T-duality transforms the bulk–boundary homomorphism into a simpler restriction map in two dimensions. In this paper, we partially generalize these results to higher dimensions in both the complex and real cases, and briefly discuss the 4D quantum Hall effect.     

Development of polyelectrolyte complexes of chitosan and phosphotungstic acid as pervaporation membranes for dehydration of isopropanol

Using a solution technique, chitosan-based polyelectrolyte complexes (PECs) were developed as pervaporation membranes by incorporating phosphotungstic acid (PTA). The resulting membranes were characterized by Fourier transform infrared spectroscopy (FTIR), wide-angle X-ray diffraction (WAXD), scanning electron microscopy (SEM) and thermogravimetric analysis (TGA). Membranes were tested for their ability to separate water–isopropanol mixtures by pervaporation in the temperature range of 30–50 °C. The experimental results demonstrated that both flux and selectivity were increased simultaneously with increasing PTA content in the membrane. The permeation flux of pure chitosan membrane was increased dramatically from 4.13 to 11.70 × 10⁻² kg/m² h and correspondingly its separation factor was increased from 4490 to 11,241 and then decreased to 7490 at 30 °C for 10 mass% of water in the feed. The total flux and flux of water were found to be almost overlapping particularly for PECs membranes, suggesting that these could be used effectively to break the azeotropic point of water–isopropanol mixtures. From the temperature dependency of diffusion and permeation values, the Arrhenius activation parameters were estimated and discussed in the context of membranes efficiency. The pure chitosan and a small amount of PTA-incorporated PECs membranes exhibited positive heat of sorption while other PECs membranes exhibited negative heat of sorption, giving exothermic contribution.     

Nonassociative Tori and Applications to T-Duality

In this paper, we initiate the study of C^*-algebras endowed with a twisted action of a locally compact abelian Lie group , and we construct a twisted crossed product , which is in general a nonassociative, noncommutative, algebra. The duality properties of this twisted crossed product algebra are studied in detail, and are applied to T-duality in Type II string theory to obtain the T-dual of a general principal torus bundle with general H-flux, which we will argue to be a bundle of noncommutative, nonassociative tori. Nonassociativity is interpreted in the context of monoidal categories of modules. We also show that this construction of the T-dual includes the other special cases already analysed in a series of papers.     

NLOphoric Triphenylamine Derived Donor‐π‐Acceptor‐π‐Donor Based Colorants: Synthesis,Spectroscopic, Density Functional Theory and Z‐scan Studies

Three Donor‐π‐Acceptor‐π‐Donor type styryl dyes ( 5a‐c ) with different secondary donors are synthesized and characterized to study their nonlinear and linear optical properties. The structure–property relationships of the dyes are described in the light of systematic photophysical and theoretical investigations. The photophysical characteristics of 5a‐c are influenced by the polarity of the medium, with an appreciable bathochromic shift in emission ( 5b = 81 nm) and large Stoke shifts ( 5b = 104–173 nm) in polar solvents. 5a‐c showed intramolecular charge transfer characteristics recognized with the help of emission solvatochromism, solvent polarity graphs, natural bond orbital analysis and HOMO–LUMO energy difference. The optimized geometry and frontier molecular orbitals reveal that the electron donation takes place from secondary donors and not from a fixed donor (triphenylamine) which is more twisted. The nonlinear optical properties obtained using solvent induced spectral shift and computational methods are found within the limiting values. Z‐scan results reveal saturable kind of behavior for 5a , 5b and 5c , whereas 5a and 5b show reverse saturable kind of behavior in acetone and ethanol and hence give optical limiting values. The two‐photon absorption cross section described by two‐level approximation is highest for 5b (251–300 GM).     

FT‐IR,FT‐Raman and DFT calculations of 3‐{[(4‐fluorophenyl)methylene]amino}‐2‐phenylquinazolin‐4(3H)‐one

Fourier transform (FT)‐Raman and Fourier transform infrared (FT‐IR) spectra of 3‐{[(4‐fluorophenyl)methylene]amino}‐2‐phenylquinazolin‐4(3H)‐one were recorded and analyzed. The vibrational wavenumbers of the title compound were computed using the B3LYP/6‐31G* basis and compared with the experimental data. The prepared compound was identified by NMR and mass spectra. The simultaneous IR and Raman activation of the CO stretching mode shows a charge transfer interaction through a π‐conjugated path. The first hyperpolarizability and infrared intensities are reported. The assignments of the normal modes are done by potential energy distribution (PED) calculations. Copyright © 2008 John Wiley & Sons, Ltd.     

FT‐IR and FT‐Raman spectra and ab initio calculations of 3‐{[(2‐hydroxyphenyl) methylene]amino}‐2‐phenylquinazolin‐4(3H)‐one

Fourier transform infrared (FT‐IR) and Fourier transform (FT) Raman spectra of 3‐{[(2‐hydroxyphenyl)methylene]amino}‐2‐phenylquinazolin‐4(3H)‐one were recorded and analyzed. The vibrational wavenumbers of the title compound were computed using HF/6‐31G* and 6‐311G* basis sets and compared with experimental data. The assignments of the normal modes are done by potential energy distribution (PED)calculations. The prepared compound was identified by nuclear magnetic resonance (NMR) and mass spectra. Optimized geometrical parameters of the title compound are in agreement with reported structures. Shortening of CN bond lengths reveal the effect of resonance. The simultaneous IR and Raman activations of the CO stretching mode shows a charge transfer interaction through a π‐conjugated path. The first hyperpolarizability, infrared intensities and Raman activities are reported. The phenyl C C stretching modes are equally active as strong bands in both IR and Raman spectra, which are responsible for hyperpolarizability enhancement leading to nonlinear optical activity. Copyright © 2009 John Wiley & Sons, Ltd.     

Mechanical properties of bulk and nanoscale TiO2 phases

The mechanical properties of bulk and nanoscale TiO₂ phases are examined with a view to assess the available bulk modulus and hardness data, and to understand the size-dependent behaviors. The bulk modulus values of thermodynamically stable bulk TiO₂ phases show a general correlation with Ti-O coordination number. As with the cotunnite-structured (OII) phase, it is likely that the seven-coordinated OI and eight-coordinated fluorite forms of TiO₂ are ultrahard substances. Of the nanoscale phases investigated thus far, nanocrystalline anatase displays the strongest size dependence of bulk modulus values, with possible stiffening behavior effected by incipient grain boundary amorphization under pressure. Nanocrystalline rutile and baddeleyite phases do not show appreciable size dependence in their compression behaviors.     

Approximating Spectral Invariants of Harper Operators on Graphs

We study Harper operators and the closely related discrete magnetic Laplacians (DML) on a graph with a free action of a discrete group, as defined by Sunada (Sun). A main result in this paper is that the spectral density function of DMLs associated to rational weight functions on graphs with a free action of an amenable discrete group can be approximated by the average spectral density function of the DMLs on a regular exhaustion, with either Dirichlet or Neumann boundary conditions. This then gives a criterion for the existence of gaps in the spectrum of the DML, as well as other interesting spectral properties of such DMLs. The technique used incorporates some results of algebraic number theory.